Systems and methods for monitoring and displaying respiratory information

ABSTRACT

Various embodiments of the present disclosure provide systems, methods and devices for respiratory support. As one example, a ventilation system is disclosed that includes a graphical display, a processor and a computer readable medium. The computer readable medium is communicably coupled to the processor and includes instructions executable by the processor to receive a measured pressure value, and receive a net flow value. The instructions are further executable to calculate a patient effort value based on a relationship between patient effort, the measured pressure value and the net flow value; and to plot the patient effort value to the graphical display.

RELATED APPLICATIONS

This application claims the benefit of U.S. Provisional Application No.61/059,599, filed Jun. 6, 2008, titled “Systems and Methods forDetermining Patient Effort and/or Respiratory Parameters in aVentilation System,” the benefit of U.S. Provisional Application No.61/101,575, filed Sep. 30, 2008, titled “Systems and Methods forMonitoring and Displaying Respiratory Information,” and the benefit ofU.S. Provisional Application No. 61/101,578, filed Sep. 30, 2008, alsotitled “Systems and Methods for Monitoring and Displaying RespiratoryInformation,” and whereby the complete disclosure of each suchapplication is hereby incorporated by reference.

BACKGROUND

The present invention is related to ventilators, and more particularlyto systems and methods for identification of time dependent signalsand/or respiratory parameters in a dynamic ventilation system.

Ventilators are designed to ventilate a patient's lungs with gas, and tothereby assist the patient when the patients ability to breathe on theirown is somehow impaired. Ventilation is achieved by providing a definedgas mixture to the patient according to a prescribed ventilationmodality. As each patient may require a different ventilation strategy,modern ventilators can be customized for the particular needs of anindividual patient.

Modern ventilators are dynamic systems whose dynamic behavior andoutputs, such as pressures and flows delivered to the patient, aredriven by input signals, such as gas flows. Proper operation of suchventilators relies on some understanding of a variety of respiratoryparameters including the resistance of the patient airways and thecompliance of the lung. These parameters may vary significantly from oneventilation system to another, and from one patient to another. In manycases, proper operation of a ventilation system is limited by theaccuracy at which such parameters are defined or estimated.

Methods for identifying the ventilation parameters for a particularindividual or a particular ventilation situation have been developed.Such methods can be divided into two different categories: staticmethods and dynamic methods. In static methods, respiratory parametersare typically estimated during short periods of induced equilibriumstates (i.e., maneuvers) of the system using only a few measurements ofquantities that are related to the estimated parameters. In contrast,dynamic methods operate to describe the dynamic behavior of the patientunder ventilation, and are typically based on continuous or segmentedcontinuous measurement of ventilator conditions. Historically,identifying respiratory parameters posed a challenge in the case of theventilation system driven by unknown input signals. This is the casewith the ventilation systems involving actively breathing patients andleaks, and many existing approaches fail to provide sufficientlyaccurate results because these signals driving the system typicallycannot be measured but they must be accounted for in the identificationalgorithms. For example, various approaches for estimating patientbreathing effort are inaccurate, and as such dynamic methods relying onan estimated patient effort are often inadequate.

In some cases, patient breathing effort has been estimated using theequation of motion, and relying exclusively on the measurement of gasflow in and out of the patient's lungs along with a pressuremeasurement. The reliability of such an approach is limited by theaccuracy at which gas flow in and out of the patient's lungs may bemeasured. Such a measurement, however, is inherently inaccurate as itrelies on a flow sensor at or near a tube inserted in the patient'strachea. The accuracy of the flow sensor is substantially reduced due tothe humidity of gas exhaled from the lung. Further, such a flow sensornear the patient's trachea is often not available in existingventilation systems.

Hence, there exists a need in the art for advanced ventilation systems,and methods for using such.

BRIEF SUMMARY

The present disclosure is related to ventilators, and more particularlyto systems and methods for controlling the delivery of gas based atleast in part on a patient's effort to breathe.

Some embodiments of the present disclosure provide ventilation systemsthat include a graphical display, a processor and a computer readablemedium. The computer readable medium is communicably coupled to theprocessor and includes instructions executable by the processor toreceive a measured pressure value and receive a net flow value. Theinstructions are further executable to calculate a patient effort valuebased on a relationship between patient effort, the measured pressurevalue and the net flow value; and to plot the patient effort value tothe graphical display. In some instances, the relationship uses a firstpatient effort value to help determine a second patient effort value. Insome instances of the aforementioned embodiments, the patient effortvalue is an estimate of actual patient effort for a particular timeinstant. In other instances, the patient effort value is the firstderivative of the actual patient effort for a particular time instant.In yet other instances, the patient effort value is the filtered patienteffort for a time instant.

In various instances of the aforementioned embodiments, the instructionsare further executable by the processor to calculate a mean time betweenbreaths, and to display the mean time between breaths to the graphicaldisplay. In one or more instances of the aforementioned embodiments, theinstructions are further executable by the processor to identify a peakbreathing effort, and to display the peak breathing effort to thegraphical display. In various instances of the aforementionedembodiments, the instructions are further executable by the processor toidentify a peak effort for a particular breath, and to display the peakeffort for the particular breath to the graphical display. In one ormore instances of the aforementioned embodiments, the instructions arefurther executable by the processor to calculate a duration of lastinspiration and/or a duration of last expiration, and to display theduration of last inspiration and/or last expiration to the graphicaldisplay.

In some instances of the aforementioned embodiments, the patient effortvalue is further based on a combination of one or more intermediatevalues calculated using the measured pressure and net flow values. Theintermediate values may be selected from an estimated normalizedprediction error (ε), a filtered pressure value (z), a regression vector(φ^(T)), and a current estimated value of a parameter vector (Θ). Insome instances of the aforementioned embodiments, the relationship usedto calculate a patient effort value is a parameterized system input tooutput relationship. In some instances, the parameterized system inputto output relationship is the regression form: z=Θ^(T)φ+φ_(d). Theparameterized input to output relationship may be derived from atransfer function, where in some instances the transfer function isderived from the model:

$\begin{bmatrix}\overset{.}{p_{Y}} \\{\overset{.}{p}}_{L}\end{bmatrix} = {\begin{bmatrix}{- \frac{1}{C_{T}R_{P}}} & \frac{1}{C_{T}R_{P}} \\\frac{1}{C_{L}R_{P}} & {- \frac{1}{C_{L}R_{P}}}\end{bmatrix}{\quad{\begin{bmatrix}p_{Y} \\p_{L}\end{bmatrix} + {\quad{{\begin{bmatrix}\frac{1}{C_{T}} & \frac{1}{C_{T}} & {- \frac{1}{C_{T}}} \\0 & 0 & 0\end{bmatrix}\begin{bmatrix}q_{AIR} \\q_{O\; 2} \\q_{E}\end{bmatrix}} + {\begin{bmatrix}0 & {- \frac{1}{C_{T}}} & 0 \\1 & 0 & {- \frac{1}{C_{T}}}\end{bmatrix}\begin{bmatrix}{\overset{.}{p}}_{P} \\q_{Tleak} \\q_{Pleak}\end{bmatrix}}}}}}}$

Other embodiments of the present disclosure provide methods forproviding graphical respiratory feedback. Such methods include measuringa pressure and providing a measured pressure; and measuring an inletflow and an outlet flow, and providing a measured net flow. Arelationship between a first value related to the measured pressure, asecond value related to the measured net flow and a third value relatedto patient effort is used to calculate an estimate of patient effort.The estimate of patient effort is displayed as a function of time via agraphical display. In some instances the methods include calculatingand/or graphically displaying various ventilation characteristics basedon or related to the estimate of patient effort. These characteristicsinclude, but are not limited to, a mean time between breaths, a peakbreathing effort, a peak effort for a particular breath, a duration oflast inspiration, a duration of last expiration, an average duration ofinspiration, and an average duration of expiration.

Yet other embodiments of the present disclosure provide ventilationsystems that include a gas inlet, a gas outlet, a tube or conduitcoupling the gas inlet and the gas outlet, a pressure sensor operable toprovide a measured pressure value indicating a pressure in the tube, afirst flow sensor operable to provide an inlet flow value indicating aflow associated with the gas inlet, a second flow sensor operable toprovide an outlet flow value indicating a flow associated with the gasoutlet, a graphical display, and a processor coupled to a computerreadable medium. The computer readable medium includes instructionsexecutable by the processor to: receive a measured pressure value andreceive a net flow value. The instructions are further executable tocalculate a patient effort value based on a relationship between patienteffort, the measured pressure value and the net flow value; and to plotthe patient effort value to the graphical display.

Yet further embodiments of the present disclosure provide ventilationsystems that include a graphical display, a processor and a computerreadable medium. The computer readable medium is communicably coupled tothe processor and includes instructions executable by the processor toreceive a measured pressure value and a net flow value. The instructionsare further executable to calculate an estimate of the respiratoryparameter based on a relationship between respiratory parameter, themeasured pressure value and the net flow value; and to plot the at leastone estimate to the graphical display. The respiratory parameter mayinclude, but is not limited to, patient resistance lung compliance,tubing compliance, patient effort and a leakage. In some instances, theestimate is displayed on the graphical display in numerical fashion, ina time plot fashion, in a bar graph, or other visual indication. Inother instances, peak and/or average values of the estimate of therespiratory characteristic is/are displayed on the graphical display. Insome instances, the estimates correspond to a first or to a particularinstance in time.

This summary provides only a general outline of some embodiments of theinvention. Many other objects, features, advantages and otherembodiments of the invention will become more fully apparent from thefollowing detailed description, the claims and the accompanyingdrawings.

BRIEF DESCRIPTION OF THE DRAWINGS

A further understanding of the various embodiments of the presentdisclosure may be realized by reference to the figures which aredescribed in remaining portions of the specification. In the figures,like reference numerals may be used throughout several of the figures torefer to similar components. In some instances, a sub-label consistingof a lower case letter is associated with a reference numeral to denoteone of multiple similar components. When reference is made to areference numeral without specification to an existing sub-label, it isintended to refer to all such multiple similar components.

FIG. 1 depicts a ventilation system including, among other things, anadaptive calculation module capable of providing adaptively estimatedrespiratory parameters and patient effort in accordance with variousembodiments of the present invention;

FIG. 2 shows a patient ventilator system and associated parameterizedmodel that may be used for determining patient effort in accordance withsome embodiments of the present invention;

FIG. 3 illustrating a graphical example of patient effort correlated toother signals that is achievable through implementation of a particularembodiment of the present invention;

FIG. 4 illustrating a flow diagram depicting a method in accordance withsome embodiments of the present invention for determining patienteffort;

FIG. 5 shows a microprocessor based system for determining patienteffort in accordance with various embodiments of the present invention;

FIG. 6 illustrating a flow diagram depicting a method in accordance withsome embodiments of the present invention for triggering a ventilationcycle;

FIG. 7 illustrating a timing diagram showing triggering of a ventilationcycle based upon an estimated patient effort signal in accordance withvarious embodiments of the present invention;

FIG. 8 illustrating timing diagrams comparing a process of triggeringoff of a pressure sensor verses a process of triggering off of anestimated patient effort signal in accordance with one or moreembodiments of the present invention;

FIG. 9 illustrating a flow diagram showing a method for providingventilation in proportion to patient effort in accordance with variousembodiments of the present invention;

FIG. 10 illustrates a group of timing diagrams that graphically depictproviding ventilation in proportion to patient effort in accordance withone or more embodiments of the present invention;

FIG. 11 shows an exemplary graphical interface showing the display ofpatient effort corresponding to an actively breathing patient inaccordance with some embodiments of the present invention; and

FIG. 12 shows an exemplary graphical interface showing the display of arespiratory parameter corresponding to an actively breathing patient inaccordance with some embodiments of the present invention.

DETAILED DESCRIPTION

The present disclosure is related to ventilators, and more particularlyto systems and methods for controlling the delivery of gas based on apatient's effort to breathe.

It is desirable to synchronize the onset and end of a ventilation cycleto effort a patient may be making to breathe on their own (i.e., patienteffort). For example, it is desirable to have an accurate ventilatortrigger, whereby the ventilator initiates a breath as soon as thepatient attempts to inhale. Some ventilators use a pressure triggerwhich senses a change in ventilation circuit pressure caused by thepatient attempting to inhale, while other ventilators use a flow triggerwhich senses a change in flow caused by the patient attempting toinhale. In either case, delays between the patient's effort and theventilator response can occur due to a variety of reasons. For example,a leak in the ventilation circuit may allow air to enter the circuitwhen the patient inhales. Since the entirety of the patient breath isnot measured by a ventilator flow sensor, and the ventilator may bemonitoring a change in flow to detect an inhalation (flow trigger), theventilator may be delayed in initiating the breath. Some embodiments ofthe present invention facilitate improved synchronization throughproviding a reasonably accurate estimate of patient effort that may beused either alone or in relation to other signals to trigger the onsetand end of a ventilation cycle. In one or more embodiments of thepresent invention, the estimated patient effort may be additionally usedin relation to controlling proportional ventilation of a patient. Suchproportional ventilation operates to deliver a gas to a patient inproportion to the patient's effort to receive such gas. In variousembodiments of the present invention, the estimated patient effortand/or respiratory parameters may be used to drive a graphical displaythat may be used by a clinician for patient monitoring and/or diagnosticpurposes.

Various embodiments of the present disclosure provide systems andmethods for estimating of one or more respiratory parameters and atleast one unmeasured input signal driving a ventilation system with areasonable degree of accuracy. In some embodiments, at least oneun-measured input signal may be derived from measured input signals,such as measured pressure and measured flow, and used to estimate therespiratory parameters. The unmeasured input signal may be, but is notlimited to, patient effort and/or a derivative of patient effort, aventilation system gas leak (i.e., a leak occurring in the tubing orpatient interface connecting a ventilator to a patient), a patient gasleak (e.g., a leak in the patient's lung), and/or flow and pressuresensing errors. The respiratory parameters may include, but are notlimited to, lung compliance (C_(L)), patient resistance (R_(P)), andtubing compliance (C_(T)). In some cases, estimation of both respiratoryparameters and the unmeasured input signal(s) is simultaneous. In someembodiments, the unmeasured input signal has a strong correlation topatient effort, and therefore can be used as a surrogate for patienteffort in subsequent ventilator actions. In other embodiments, methodsof the present invention allow the respiratory parameters to becontinuously provided. In this manner, patient effort may be determined,as well as respiratory or ventilation system parameters such as lungcompliance, patient resistance, leak, etc.

In some embodiments of the present invention, a relationship betweenmeasurable pressure, measurable flow and an unknown patient effort isexploited to provide a continuous estimate of patient effort along witha variety of respiratory parameters. In particular instances, therelationship is defined as a transfer function relating, inter alia,measured pressure, measured flow and patient effort. In such cases, thetransfer function may be reduced using linear regression techniques toyield one or more interim values that may in turn be used to estimatepatient effort. In an embodiment, ongoing inputs of measured pressureand measured flow are plugged into the transfer function to estimatepatient effort and, as needed, one or more respiratory parameters. Inanother embodiment, the estimate of patient effort may be usedrecursively to derive a more accurate estimate of patient effort duringsucceeding calculation periods. Thus, through use of recursion, theaccuracy of an estimated patient effort value may be continuouslyimproved.

In some cases, the measured flow is a net flow value that combines a netflow of gas out of the system with a net flow of gas into the system. Inone particular case, the net flow of gas into the system includes a flowof Oxygen combined with a flow of Air into the system. Such flows arereasonably easy to measure, and are not subject to the inaccuracies thatoften attend the measurement of gas flow near the lung.

In some cases, a patient effort signal or some proxy thereof calculatedas described above may be used to trigger a ventilation cycle. Use ofsuch signals can allow a ventilation system to more accuratelysynchronize mechanical ventilation with the efforts being made by apatient to breathe on their own.

Of note, the respiratory parameters and the derivative of patient effortmay be inputs to the same model, and may be calculated usinginterdependent equations derived from that same model. As the valuescalculated from some of the interdependent equations are used as inputsto other interdependent equations, they may be generically referred toas interim values. As used herein, the phrase “interim value” is used inits broadest sense to mean a value derived from one equation that isused as an input to another equation. It will be noted based on readingthis disclosure that a variety of interim values may be utilized inrelation to the various embodiments of the present invention.

Turning to FIG. 1, a ventilation system 1 is shown in accordance withvarious embodiments of the present invention. Ventilation system 1includes a ventilator 10, an adaptive calculation module 20, a graphicaluser interface 40, and a proportional and triggering control module 30.Ventilator 10 may be any ventilator known in the art that is capable ofproviding a measured pressure 65, a measured inlet flow 70 and ameasured outlet flow 75. Adaptive calculation module 20 receivespressure 65, inlet flow 70 and outlet flow 75 and calculates anestimated patient effort 55 and estimated respiratory parameters 60.Patient effort 55 may be patient effort itself or some signal that isstrongly correlated to patient effort. Signals correlated to patienteffort are more fully discussed below. Respiratory parameters 60 mayinclude a variety of parameters that are more fully described below. Inan embodiment, the calculations performed by adaptive calculation module20 may be adaptive in nature relying on previous interim values togenerate updated respiratory parameters 60 and patient effort 55estimates. In some embodiments, such interim values may include thepatient effort 55 and/or the respiratory parameter estimates 60 as shownby dashed lines in FIG. 1. Alternatively (not shown), the previousinterim values used by adaptive calculation module 20 may be compositeparameters that do not directly correspond to any identifiablerespiratory parameter (such as, for example, the covariance matrix andparameter vector discussed in greater detail below).

In the embodiment illustrated, patient effort 55 is provided toproportional and triggering control module 30. Based on patient effort55, proportional and triggering control module 30 generates one or morecontrol signals 80 that are provided to ventilator 10. In someembodiments, control signals 80 control the timing of gas delivery to apatient. In various embodiments, control signals 80 control the amountof gas to be delivered to a patient, where the amount of gas is inproportion to patient effort 55.

Ventilator 10 provides control signals 90 that drive graphical userinterface 40. Graphical user interface 40 may be included as part ofventilator 10 to allow for interaction with a user including, but notlimited to, receiving user commands and/or displaying data relevant toventilator operation. In some embodiments, ventilator 10 may directgraphical user interface 40 to display information 85 provided byadaptive calculation module 20. Such information may include, but is notlimited to, respiratory parameters 60 and/or patient effort 55 as ismore fully discussed below.

Various embodiments of the present invention utilize a parameterizeddynamic model of a patient ventilator system to determine patienteffort. A model of a ventilator system 100 is depicted in FIG. 2.Ventilator system 100 includes an inlet air flow 105 (q_(AIR)), an inletOxygen flow 110 (q_(O2)), and an outlet gas flow 115 (q_(E)). It shouldbe noted that while ventilator system 100 shows two gas sources, Air andOxygen, more or fewer inlet gas sources may be used in relation todifferent embodiments of the present invention. For example, it may bethat only an Air source is used, or that in addition to the inlet Airsource and the inlet Oxygen source, a Helium and/or Heliox source may beincluded. Based on the disclosure provided herein, one of ordinary skillin the art will recognize a variety of other gas sources that may beused in relation to different embodiments of the present invention.

Tubing, flow valves, and/or pressure monitors included in the systemintroduce some resistance to gas flow in ventilator system 100. Inparticular, an air resistance 120 (R_(air)), an Oxygen resistance 125(R_(O2)), an exhalation resistance 130 (R_(EV)), and a patientresistance 135 (R_(P)) (i.e., some combination of trachea resistance andresistance in an endotracheal tube) are possible. A pressure sensor 150measures the pressure (p_(I)) at the inlet at a location where the airflow and Oxygen flow is combined, and a pressure sensor 155 measures thepressure (p_(E)) in an exhalation output. It should be noted thatpressure sensor 150 may be replaced by individual pressure sensorsassociated with respective inlet lines. The pressure (p_(Y)) at alocation where inlet and outlet gases combine is represented as abaffles 140 (e.g., wye gas pressure), and the pressure (p_(L)) in thepatient's lungs is represented by another baffles. In some embodimentsof the present invention, p_(Y) is determined though use of a pressuremeasurement device mounted at or near the particular locationcorresponding to the pressure. In other embodiments of the presentinvention, p_(Y) is set equal to either p_(I) or p_(E), while in otherembodiments of the present invention, p_(Y) is set to the average ofp_(I) and p_(E). In any of the aforementioned three cases, p_(Y) isconsidered to be “directly measured” as it is either a measurement or isan average of other direct measurements. A gas flow associated with aleakage 160 (q_(Tleak)) in the tubing, and a gas flow associated with aleakage 165 (q_(Pleak)) in the patient are also identified. A patienteffort value 195 (p_(P)) is shown as a force interacting with the forceof moving gas in and out of a patient's lung.

Various equations may be used to describe the operation of ventilatorsystem 100. For example, using the principle of conservation of mass,the various flow values (i.e., q_(AIR), q_(O2), q_(T), q_(Tleak), q_(P),q_(Pleak), q_(LUNG), q₁) may be combined to yield the following threeequations:q _(LUNG) =q _(p) −q _(Pleak);q ₁ −q _(p) −q _(E)=0; andq _(AIR) +q _(O2) =q ₁ +q _(Tleak) +q _(T).Further, using the principle of equilibrium of forces, the pressuresp_(Y), P_(L) and p_(p) and flows q_(T) and q_(L) can be combined in thefollowing relationships:

${p_{Y} = {\frac{1}{C_{T}}{\int{q_{T}{\mathbb{d}t}}}}},{{{{or}\mspace{14mu}{\overset{.}{p}}_{Y}} = {\frac{1}{C_{T}}q_{T}}};}$${{{{and}\mspace{14mu} p_{P}} - p_{L}} = {\frac{1}{C_{L}}{\int{q_{L}{\mathbb{d}t}}}}},{{{or}\mspace{14mu}{\overset{.}{p}}_{L}} = {{\overset{.}{p}}_{L} = {{\overset{.}{p}}_{p} - {\frac{1}{C_{L}}{q_{L}.}}}}}$Finally, the relationship between pressure and flow can be used toderive the following equation based on ventilator system 100:p _(Y) −p _(L) =R _(P) ·q _(P).By algebraically manipulating the aforementioned equations derived fromventilator system 100 and recasting the equations in a matrix form, thefollowing parameterized model 190 is developed to characterize theoperation of ventilator system 100 of FIG. 2:

$\begin{bmatrix}\overset{.}{p_{Y}} \\{\overset{.}{p}}_{L}\end{bmatrix} = {\begin{bmatrix}{- \frac{1}{C_{T}R_{P}}} & \frac{1}{C_{T}R_{P}} \\\frac{1}{C_{L}R_{P}} & {- \frac{1}{C_{L}R_{P}}}\end{bmatrix}{\quad{\begin{bmatrix}p_{Y} \\p_{L}\end{bmatrix} + {\quad{{{\begin{bmatrix}\frac{1}{C_{T}} & \frac{1}{C_{T}} & {- \frac{1}{C_{T}}} \\0 & 0 & 0\end{bmatrix}\begin{bmatrix}q_{AIR} \\q_{O\; 2} \\q_{E}\end{bmatrix}} + {\begin{bmatrix}0 & {- \frac{1}{C_{T}}} & 0 \\1 & 0 & {- \frac{1}{C_{T}}}\end{bmatrix}\begin{bmatrix}{\overset{.}{p}}_{P} \\q_{Tleak} \\q_{Pleak}\end{bmatrix}}},}}}}}$where {dot over (p)}_(Y) is the first derivative of the pressuremeasured at the tubing branch, {dot over (p)}_(L) is the firstderivative of the pressure in the patient's lung, {dot over (p)}_(P) isthe first derivative of the patient effort, C_(T) represents tubingcompliance, and C_(L) represents lung compliance. It should be notedthat where more or fewer inlet gases are utilized, that parameterizedmodel 190 may be modified to account for the different gases inaccordance with other embodiments of the present invention.

Various embodiments of the present invention utilize parameterized model190 to determine patient effort, p_(P). In different embodiments of thepresent invention, assumptions may be made to simplify the calculation.In one particular embodiment of the present invention, leakage 160 maybe assumed to exhibit the following linear relationship between thetubing leak flow and the pressure drop across an opening:

$q_{Tleak} = {{\frac{1}{R_{LEAK}}p_{y}} = {\lambda_{LEAK}{p_{y}.}}}$

It should be noted that in other embodiments of the present invention,other assumptions about the relationship between the tubing leak flowand the pressure drop across an opening may be used. Relying on theaforementioned linear assumption for the tubing leak flow, parameterizedmodel 190 may be reduced to the following model:

$\begin{bmatrix}{\overset{.}{p}}_{Y} \\{\overset{.}{p}}_{L}\end{bmatrix} = {{\begin{bmatrix}{{- \frac{1}{C_{T}R_{P}}} - \frac{\lambda_{Tleak}}{C_{T}}} & \frac{1}{C_{T}R_{P}} \\\frac{1}{C_{L}R_{P}} & {- \frac{1}{C_{L}R_{P}}}\end{bmatrix}\left\lbrack \begin{matrix}p_{Y} \\p_{L}\end{matrix} \right\rbrack} + {\quad{{\begin{bmatrix}\frac{1}{C_{T}} & \frac{1}{C_{T}} & {- \frac{1}{C_{T}}} \\0 & 0 & 0\end{bmatrix}\begin{bmatrix}q_{AIR} \\q_{02} \\q_{E}\end{bmatrix}} + {\begin{bmatrix}0 & 0 \\1 & {- \frac{1}{C_{L}}}\end{bmatrix}\begin{bmatrix}{\overset{.}{p}}_{P} \\q_{Pleak}\end{bmatrix}}}}}$

Based on the aforementioned parameterized model, the transfer functionfor p_(Y) is defined as follows:

$\begin{matrix}{{p_{Y}(s)} = {{\frac{b_{q}(s)}{a(s)}\left( {{q_{AIR}(s)} + {q_{02}(s)} - {q_{E}(s)}} \right)} + {\frac{b_{Pp}(s)}{a(s)}{{\overset{.}{p}}_{P}(s)}} +}} \\{\frac{b_{Pleak}(s)}{a(s)}{q_{Pleak}(s)}} \\{{= {{\frac{b_{q}(s)}{a(s)}{q_{N}(s)}} + {\frac{b_{Pp}(s)}{a(s)}{{\overset{.}{p}}_{P}(s)}} + {\frac{b_{Pleak}(s)}{a(s)}{q_{Pleak}(s)}}}},}\end{matrix}$where the instantaneous sum of each of the measured flows (e.g.,q_(AIR)+q_(O2)−q_(E)) is denoted q_(N) for net flow

$\frac{b_{q}(s)}{a(s)}{q_{N}(s)}$represents a transfer function from the net flow (q_(N)) to the output(p_(Y)),

$\frac{b_{Pp}(s)}{a(s)}{{\overset{.}{p}}_{P}(s)}$represents a transfer function from the derivative of patient effort({dot over (p)}_(P)) to the output (p_(Y)), and

$\frac{b_{Pleak}(s)}{a(s)}{q_{Pleak}(s)}$represents a transfer function from patient leakage (q_(Pleak)) to theoutput (p_(Y)). It should be noted that the first term in the precedingtransfer function (i.e., the q_(N) term) is a transfer function relatedto a known, measured value, and the second term in the precedingtransfer function (i.e., the p_(p) term) is a transfer function relatedto an unknown, adaptively estimated value. In some embodiments of thepresent invention, the third term (i.e., the q_(Pleak) term is assumedto be zero for the sake of simplification. Again, using the abovementioned parameterized model, the relationships between the transferfunction coefficients and the system parameters are as follow:

${{a(s)} = {{s^{2} + {\frac{C_{L} + C_{T} + {C_{L}R_{P}\lambda_{Tleak}}}{C_{L}C_{T}R_{P}}s} + \frac{\lambda_{Tleak}}{C_{L}C_{T}R_{P}}} = {s^{2} + {a_{1}s} + a_{0}}}},{with}$${a_{1} = \frac{C_{L} + C_{T} + {C_{L}R_{P}\lambda_{Tleak}}}{C_{L}C_{T}R_{P}}},{a_{0} = \frac{\lambda_{Tleak}}{C_{L}C_{T}R_{P}}}$${{b_{q}(s)} = {{{\frac{1}{C_{T}}s} + \frac{1}{C_{L}C_{T}R_{P}}} = {{b_{q\; 1}s} + b_{q\; 0}}}},{with}$${b_{q\; 1} = \frac{1}{C_{T}}},{b_{q\; 0} = \frac{1}{C_{L}C_{T}R_{P}}}$${b_{Pp}(s)} = {\frac{1}{C_{T}R_{P}} = b_{{Pp}\; 0}}$${b_{Pleak}(s)} = {\frac{1}{C_{L}C_{T}R} = b_{{Pleak}\; 0}}$

From the forgoing, it is possible to derive a parameterized output modelin a linear regression form. A first step in defining the parameterizedlinear regression output model includes defining an unknown parametervector such as the following:Θ^(T) =[a ₀ a ₁ b _(q0) b _(q1)].From the unknown parameter model, once estimated, all lumped parametersof ventilator system 100 (e.g., C_(T), C_(L), R_(P), and λ_(LEAK)) maybe recovered. Through algebraic manipulation of the transfer functionfor p_(Y) may be represented as:

${{p_{Y}(s)}\frac{s^{2}}{\Lambda(s)}} = {{{- {p_{Y}(s)}}\frac{\left( {{a_{1}s} + a_{0}} \right)}{\Lambda(s)}} + {{b_{q}(s)}\frac{q_{N}(s)}{\Lambda(s)}} + {{b_{Pp}(s)}\frac{{\overset{.}{p}}_{P}(s)}{\Lambda(s)}} + {{b_{Pleak}(s)}{\frac{q_{Pleak}(s)}{\Lambda(s)}.}}}$In this case, the pressure

${p_{Y}(s)}\frac{s^{2}}{\Lambda(s)}$represents pressure p_(Y)(s) after filtering through a proper filter,

$\frac{s^{2}}{\Lambda(s)}.$Such a proper filter relies on a polynomial Λ(s) that is the same or ofhigher order than s² (e.g., s², s³, s⁴ . . . ). By assuming that patientleakage (q_(Pleak)) is zero, a compact linear regression form of theinput to output relationship corresponding to parameterized model 190 ofventilation system 100 is represented as:

z = Θ^(T)φ + φ_(d) $z = {{p_{Y}(s)}\frac{s^{2}}{\Lambda(s)}}$$\Theta^{T} = \begin{bmatrix}a_{0} & a_{1} & b_{q\; 0} & b_{q\; 1}\end{bmatrix}$ $\varphi^{T} = \begin{bmatrix}{- \frac{p_{Y}(s)}{\Lambda(s)}} & {- \frac{{p_{Y}(s)}s}{\Lambda(s)}} & \frac{q_{N}(s)}{\Lambda(s)} & \frac{{q_{N}(s)}s}{\Lambda(s)}\end{bmatrix}$$\varphi_{d} = {{b_{Pp}(s)}\frac{{\overset{.}{p}}_{P}(s)}{\Lambda(s)}}$where z is the output pressure value, φ^(T) is the regression vectorrepresenting a collection of known signals, and φ_(d) is filteredpatient effort.

In this case, use of standard linear regression to estimate the systemparameters Θ^(T)=[a₀ a₁ b_(q0) b_(q1)] is not possible as φ_(d) isunknown. By inspecting the unknown term

${\varphi_{d} = {{b_{Pp}(s)}\frac{{\overset{.}{p}}_{P}(s)}{\Lambda(s)}}},$and understanding that the derivative of patient effort ({dot over(p)}_(P)) is a bounded signal, that the filter (Λ(s)) is a stablepolynomial, and

$\frac{b_{Pp}(s)}{\Lambda(s)}$is a proper linear filter, it is apparent that the unknown filteredpatient effort (i.e., φ_(d)) is a smooth signal. Based on thisunderstanding, the value of the unknown filtered patient effort at anytime t can be approximated by its value at the time t-dt, where dtrepresents an infinitesimal or finite, but small amount of time:φ_(d)≈φ_(d) e ^(−s·dt) =e ^(−s·dt)(z−Θ ^(T)φ).In some embodiments of the present invention, dt is five milliseconds orless. The aforementioned approximation represents a reasonable guess, orprediction, of the unknown filtered patient effort signal at time t thatmay be used in calculating respiratory parameters, and thereafter incalculating patient effort. This reasonable guess can be used todetermine the predicted value ({circumflex over (z)}) of the systemoutput (z) can be defined in accordance with the following equation:{circumflex over (z)}=Θ ^(T) φ+e ^(−s·dt)(z−Θ ^(T)φ)=Θ^(T)(φ−e^(−s·dt)φ)+e ^(−s·dt) z.From this definition, the parametric identification problem can besolved through formulation of the following problem: Given φ(t), z(t),find

${\Theta = {\arg\left\lfloor {\min\limits_{\Theta}{J\left( {z - \hat{z}} \right)}} \right\rfloor}},$where J( ) is a convex (e.g., ( )²) function of Θ. From this point oneof a number of mathematical solutions may be applied to resolve theproblem. As one example, a modified recursive least squares method maybe used. More detail related to a non-modified mathematicalimplementation of such an approach is more fully described in one orboth of (1) Lennart Ljung, “System Identification, Theory for the User”,Second Edition, Prentice Hall, 1999 (ISBN 0-13-656695-2) and (2) PetrosIoannou and Jing Sun, Robust Adaptive Control, Prentice Hall, 1995 (ISBN9780134391007). Both of the aforementioned references are incorporatedherein by reference for all purposes.

In implementing a modified recursive least squares method, a predictionerror (ε) is first normalized and signals are adopted for the normalizedsignals as set forth in the following equation:

$\begin{matrix}{ɛ = \frac{z - {\hat{z}(t)}}{m^{2}}} \\{= \frac{z - {\Theta^{T}\left( {\varphi - {{\mathbb{e}}^{{- s} \cdot {dt}}\varphi}} \right)} - {{\mathbb{e}}^{{- s} \cdot {dt}}z}}{m^{2}}} \\{= \frac{{z\left( {1 - {\mathbb{e}}^{{- s} \cdot {dt}}} \right)} - {\Theta^{T}{\varphi\left( {1 - {\mathbb{e}}^{{- s} \cdot {dt}}} \right)}}}{m^{2}}} \\{= \frac{\overset{\sim}{z} - {\Theta^{T}\overset{\sim}{\varphi}}}{m^{2}}}\end{matrix}$$\overset{\sim}{z} = {z\left( {1 - {\mathbb{e}}^{{- s} \cdot {dt}}} \right)}$$\overset{\sim}{\varphi} = {\varphi\left( {1 - {\mathbb{e}}^{{- s} \cdot {dt}}} \right)}$$m^{2} = {1 + {{\overset{\sim}{\varphi}}^{T}\overset{\sim}{\varphi}}}$where ε is the normalized prediction error, {tilde over (z)} and {tildeover (φ)} are the differences of the output and regressor respectivelycorresponding to the time interval dt, and m is the normalizationsignal. In addition, a modified function J( ) (referred to as a costfunction) is adopted in accordance with the following equation:

${{J\left( {\Theta(t)} \right)} = {{\frac{1}{2}{\int_{0}^{t}{{\mathbb{e}}^{- {\beta{({t - \tau})}}}\frac{\left( {\overset{\sim}{z} - {\Theta^{T}\overset{\sim}{\varphi}}} \right)^{2}}{m^{2}}\ {\mathbb{d}\tau}}}} + {\frac{1}{2}{{\mathbb{e}}^{{- \beta}\; t}\left( {\Theta - \Theta_{0}} \right)}^{T}Q_{0}\left( {\Theta - \Theta_{0}} \right)}}},$where β>0 and Q₀≧0 are referred to as a forgetting factor and a penaltymatrix. Based on this, the following stationary conditions must be metat the solution Θ:

$\begin{matrix}{{{\frac{\partial}{\partial\Theta}{J\left( {\Theta(t)} \right)}} = {{{\mathbb{e}}^{{- \beta}\; t}{Q_{0}\left( {\Theta - \Theta_{0}} \right)}} - {\int_{0}^{t}{{\mathbb{e}}^{- {\beta{({t - \tau})}}}\ \frac{\overset{\sim}{z}\overset{\sim}{\varphi}}{m^{2}}{\mathbb{d}\tau}}} +}}\ } \\{{\int_{0}^{t}{{\mathbb{e}}^{- {\beta{({t - \tau})}}}\frac{\overset{\sim}{\varphi}{\overset{\sim}{\varphi}}^{T}}{m^{2}}{\mathbb{d}\tau}\;\Theta}} =} \\{= {{\left\lbrack {{{\mathbb{e}}^{{- \beta}\; t}Q_{0}} + {\int_{0}^{t}{{\mathbb{e}}^{- {\beta{({t - \tau})}}}\frac{\overset{\sim}{\varphi}\overset{\sim}{\varphi}}{m^{2}}{\mathbb{d}\tau}}}} \right\rbrack\Theta} -}} \\{\left\lbrack {{{\mathbb{e}}^{{- \beta}\; t}Q_{0}\Theta_{0}} + {\int_{0}^{t}{{\mathbb{e}}^{- {\beta{({t - \tau})}}}\ \frac{\overset{\sim}{z}\overset{\sim}{\varphi}}{m^{2}}{\mathbb{d}\tau}}}} \right\rbrack =} \\{= {{P^{- 1}\Theta} - \left\lbrack {{{\mathbb{e}}^{{- \beta}\; t}Q_{0}\Theta_{0}} + {\int_{0}^{t}{{\mathbb{e}}^{- {\beta{({t - \tau})}}}\ \frac{\overset{\sim}{z}\overset{\sim}{\varphi}}{m^{2}}{\mathbb{d}\tau}}}} \right\rbrack}} \\{= 0}\end{matrix}$

Thus, Θ can be found non-recursively as:

${\Theta = {P\left\lbrack {{{\mathbb{e}}^{{- \beta}\; t}{Q_{0}\left( {\Theta - \Theta_{0}} \right)}} + {\int_{0}^{t}{{\mathbb{e}}^{- {\beta{({t - \tau})}}}\ \frac{\overset{\sim}{z}\overset{\sim}{\varphi}}{m^{2}}{\mathbb{d}\tau}}}} \right\rbrack}},{{where}\text{:}}$$P = {\left\lbrack {{{\mathbb{e}}^{{- \beta}\; t}Q_{0}} + {\int_{0}^{t}{{\mathbb{e}}^{- {\beta{({t - \tau})}}}\ \frac{\overset{\sim}{\varphi}{\overset{\sim}{\varphi}}^{T}}{m^{2}}{\mathbb{d}\tau}}}} \right\rbrack^{- 1}.}$Matrix P and vector Θ satisfy the following two differential equationswhich complete the definition of the recursive algorithm that can beused to solve the parameter identification problem:

${\overset{.}{P} = {{\beta\; P} - {P\ \frac{\overset{\sim}{\varphi}{\overset{\sim}{\varphi}}^{T}}{m^{2}}P}}},{{P(0)} = {P_{0} = Q_{0}^{- 1}}}$${\overset{.}{\Theta} = {P\; ɛ\;\overset{\Cap}{\varphi}}},$where ε is the normalized error or difference between the last measuredvalues and current measured values.

In the following discussion, methods are described that can be used toindirectly estimate a current value of patient effort in real time. Inaddition, it is demonstrated how various combinations of the abovementioned interim values (e.g., signals internal the transfer function)explained above possess a significant level of correlation with theunmeasured patient effort. Because of the correlation, the interimvalues may be used to characterize patient effort with a reasonabledegree of accuracy.

From the relationships established above, it is clear that:

$\varphi_{d} = {\left( {z - {\Theta^{T}\varphi}} \right) = {{b_{Pp}(s)}{\frac{{\overset{.}{p}}_{P}(s)}{\Lambda(s)}.}}}$

By choosing an appropriate filter,

$\frac{1}{\Pi(s)},$that yields

${\frac{\Lambda(s)}{b_{Pp}(s)}\frac{1}{\Pi(s)}},$an estimate of the derivative of patient effort ({dot over ({circumflexover (p)}_(P)) of the real derivative of patient effort ({dot over(p)}_(P)) can be computed as follows:

${{\hat{\overset{.}{p}}}_{P}(s)} = {\left( {z - {\Theta^{T}\varphi}} \right)\frac{\Lambda(s)}{b_{Pp}(s)}{\frac{1}{\Pi(s)}.}}$

Based on the following equation, it is apparent that a prediction errorsignal, z−{circumflex over (z)}, is correlated with the patient effortsignal, {dot over (p)}_(P), and the filtered version thereof, φ_(d):

${z - \overset{\Cap}{z}} = {{{\Theta^{T}\varphi} + \varphi_{d} - \left( {{\Theta^{T}\varphi} + {{\mathbb{e}}^{{- s} \cdot {dt}}\left( {z - {\Theta^{T}\varphi}} \right)}} \right)}\mspace{50mu} = {{\varphi_{d} - {{\mathbb{e}}^{{- s} \cdot {dt}}\varphi_{d}}}\mspace{50mu} = {d\frac{\varphi_{d}\left( {t - {\mathbb{d}t}} \right)}{\mathbb{d}t}{{\mathbb{d}t}.}}}}$

Using the transfer function defined above and the current estimate ofthe parameter vector Θ, a prediction ({circumflex over (p)}_(y)) of thecurrent pressure in the tubing (p_(y)) is represented by the followingequation:

${{\hat{p}}_{Y}\left( {s,\Theta} \right)} = {\frac{b_{q}\left( {s,\Theta} \right)}{a\left( {s,\Theta} \right)}{{q_{N}(s)}.}}$

From this, the prediction error may be described by the followingequation:

${{p_{y} - {\hat{p}}_{y}} = {\frac{b_{Pp}(s)}{a(s)}{\overset{.}{p}}_{P}(s)}},$Which is a filtered version of the derivative of patient effort ({dotover (p)}_(P)). Moreover, if the ventilation system is characterized bythe absence of tubing leaks (i.e., assume λ_(LEAK)=0), then theprediction error, p_(y)−{circumflex over (p)}_(y) resembles the patienteffort signal (p_(P)) as the transfer function

$\frac{b_{Pp}(s)}{a(s)}$is an integration function.

The aforementioned equations describe relationships between patienteffort (i.e., p_(P) and/or {dot over (p)}_(P)), and accuratelyobtainable flow and pressure measurements. FIG. 3 graphically depictsthe exemplary correlation between patient effort (i.e., p_(P) and/or{dot over (p)}_(P)) and exemplary signals internal to the previouslydescribed algorithm. As shown, a timing diagram 210 depicts patienteffort (p_(P)) as a function of time. A timing diagram 205 depicts thefirst derivative of patient effort ({dot over (p)}_(P)) as a function oftime. A timing diagram 215 depicts p_(y)−{circumflex over (p)}_(y) and atiming diagram 220 depicts z−{circumflex over (z)}. The magnitude ofeach of p_(P), {dot over (p)}_(P), p_(y)−{circumflex over (p)}_(y) andz−{circumflex over (z)} is represented in centimeters of H₂O. As wouldbe expected based on the analysis provided above, there is a strongcorrelation between patient effort (p_(P)) depicted in diagram 210 andthe signal p_(y)−{circumflex over (p)}_(y) depicted in diagram 215.Similarly, diagrams 205 and 220 demonstrate a strong correlation betweenthe first derivative of the patient effort, {dot over (p)}_(P), and thesignal z−{circumflex over (z)}. Thus, the reconstructed signals can beused to predict the otherwise unknown signals {dot over (p)}_(P) andp_(P). It should be noted that the results are merely exemplary, andthat based on the disclosure provided herein, one of ordinary skill inthe art will recognize a variety of different signals and their delayedversions that may be achieved through use of different embodiments ofthe present invention to characterize the unknown patient effort signalsand the derivatives thereof.

Turning to FIG. 4, a flow diagram 300 depicts a method in accordancewith some embodiments of the present invention for determining patienteffort. A ventilator system is provided that includes a ventilator thatis coupled to a subject using various tubing. The ventilator receivesone or more inlet gas flows and includes an outlet gas flow in additionto an inlet/outlet to the subject. Following flow diagram 300, pressurein the tubing (p_(y)) is measured along with the inlet flow(s) and theoutlet flow to generate a net flow (q_(n)) (block 305). The pressurevalue p_(y) is filtered and provided as an output (z) (block 310), andthe pressure (p_(y)) and net flow value (q_(n)) are filtered andcombined in a regression vector (φ^(T)) (block 315). Differences and/orderivatives of the aforementioned values (i.e., z and φ^(T)) arecalculated to generate outputs m², {tilde over (z)} and {tilde over (φ)}(block 320). In addition, time delayed versions of z (i.e., ze^(−sdt))and {tilde over (φ)} (i.e., {tilde over (φ)}e^(−sdt)) are created(blocks 317, 318). m², {tilde over (z)}, {tilde over (φ)} and Θ^(T) arecombined to generate an estimated normalized prediction error (ε) (block325); and m², {tilde over (φ)} and ε are used along with a previouslycomputed covariance matrix (P₀) to calculate an updated covariancematrix (P) (block 330). The newly calculated covariance matrix (P) isstored and maintained as the previously computed covariance (P₀) for usein later updating of the covariance matrix (block 335). The updatedcovariance matrix (P) is used along with the previously computed ε and{tilde over (φ)} values to calculate an updated system parameter vector(Θ) (block 340). In addition, a time delayed version of Θ (i.e.,Θe^(−sdt)) generated (block 319). As discussed above, the systemparameter vector (Θ) incorporates various system parameters including,for example, tubing compliance (C_(T)), lung compliance (C_(L)), lumpedresistance (R_(P)), and leakage (λ_(LEAK)).

During the above mentioned processing (blocks 305-340), various of theinterim values may be used either separately or in combination toestimate patient effort (block 345). For example, as depicted in FIG. 3above, z correlates to patient effort. Further, as z may be calculatedusing other constituent elements, the constituent elements may also beused to estimate patient effort. Based on the disclosure providedherein, one of ordinary skill in the art will recognize other uses ofthe constituent elements to predict patient effort.

Turning to FIG. 5, a microprocessor based system 400 for determiningpatient effort is depicted in accordance with various embodiments of thepresent invention. System 400 includes a microprocessor 410 communicablycoupled to a computer readable medium 460. Microprocessor 410 may be anyprocessor known in the art that is capable of receiving various inputvalues, and executing software or firmware instructions to provide anoutput based on the input values. Computer readable medium 460 may beany media capable of storing instructions that are executable bymicroprocessor 410. Based on the disclosure provided herein, one ofordinary skill in the art will recognize a variety of processors thatmay be used in relation to different embodiments of the presentinvention. As just some examples, computer readable medium 460 may be ahard disk drive, a tape drive, a portable solid state memory, a CD ROM,a RAM, combinations of the aforementioned, or the like. Based on thedisclosure provided herein, one of ordinary skill in the art willrecognize a variety of media and combinations of the media that may beused in relation to different embodiments of the present invention.

Instructions 450 when executed cause microprocessor 410 to receivevarious I/O via an I/O interface 420. The received I/O include measuredinlet gas flows 422, 424, and a measured outlet gas flow 426. In somecases, the measured inlet gas flows measure the flow of Air and Oxygen,respectively. It should be noted that more or fewer than two inlet gasflows may be measured depending upon the particular embodiment of thepresent invention. Outlet gas flow 426 measures the gas flow beingexhaled from system 400. Further, the received I/O include measuredinlet gas pressures 428, 430 associated with the respective inlet gasflows 422, 424. It should be noted that where there are more or fewerinlet gas flows that the I/O may include more or fewer measured gaspressure inputs. Further, in some embodiments of the present invention,a single gas pressure input may be provided in place of inlet gaspressures 428, 430 where a single gas pressure sensor is placed insystem 400 at a location that allows it to provide a pressure value thateffectively combines inlet gas pressures 428, 430. Further, instructions450 when executed cause microprocessor 410 to implement a patient effortalgorithm using the I/O received via I/O interface 420, and providing apatient effort output 440. Such a patient effort algorithm may be, butis not limited to, the patient effort algorithms discussed above inrelation to FIG. 2 and FIG. 4. As part of implementing the patienteffort algorithm, instructions 450 cause microprocessor 410 to calculatea variety of otherwise unknown system parameters including, but notlimited to, tubing compliance 412 (C_(T)), lung compliance 414 (C_(L)),lumped resistance 416 (R_(P)), and leakage 418 (λ_(LEAK)). Theaforementioned system parameters may be used in a variety of interimcalculations with the results of one or more of the interim calculationsproviding results that are predictive of patient effort output 440.

In addition, microprocessor based system 400 may include a graphicaluser interface driver 490 and a graphical user interface 495. Graphicaluser interface 495 may be any interface that provides for graphicallyportraying information from microprocessor based system 400 to a user.Thus, graphical user interface 495 may be any display known in the art.In some cases, graphical user interface 495 may further include anability to receive input from a user. The ability to receive input maybe provided by, for example, a touch screen capability, a keyboard, amouse, and/or the like deployed in association with graphical userinterface 495. Graphical user interface driver 490 may be any circuit,system or device known in the art that is capable of convertinginformation from microprocessor based system 400 into graphicalinformation displayable via graphical user interface 495.

FIG. 6 is a flow diagram 500 depicting a method in accordance with someembodiments of the present invention for triggering a ventilation cycle.Following flow diagram 500, a pressure is measured (block 505), an inletflow is measured (block 510), and an outlet flow is measured (block515). In some cases, the pressure is measured in a tube connecting aventilator to a person being ventilated. In some cases, the pressure ismeasured near a gas inlet and/or near a gas outlet. In other cases, thepressure is measured near a junction of the gas inlet with the gasoutlet. In various cases, the pressure measurement is a single pointpressure measurement, while in other cases the pressure measurement is amultiple point pressure measurement and the measured pressure is amathematical combination of two or more pressure measurements. Measuringthe inlet now may include measuring the flow of a single gas, ormeasuring the flows of two or more gases and aggregating the multipleflow values. Measuring the outlet flow may include, but is not limitedto, measuring the flow of gas at the outlet of the ventilation system.The outlet flow is subtracted from the inlet flow at a particularinstance to generate an instantaneous net flow (block 520).

The net flow and measured pressure for a given instant are used tocalculate an updated prediction of patient effort (block 525). Thisprocess may be done using the approach discussed above in relation toFIG. 4. It is then determined whether the updated prediction of patienteffort indicates an onset condition (block 530). Where an onsetcondition is indicated (block 530), a ventilation cycle is triggered tobegin (block 535). As an example, the updated prediction of patienteffort may be the filtered patient effort signal (φ_(d)) that wasdiscussed above. The filtered patient effort signal is a function of thederivative of patient effort ({dot over (p)}_(p)) as set forth in thefollowing equation:

$\varphi_{d} = {{b_{Pp}(s)}{\frac{{\overset{.}{p}}_{P}(s)}{\Lambda(s)}.}}$Thus, the filtered patient effort signal is expected to be negative whenthe actual patient effort (p_(p)) is decreasing. Therefore, the onset ofinspiration is indicated when the filtered patient effort signal becomesless than zero (e.g., exhibits a negative zero crossing where the signaltransitions from a positive value to a negative value). This indicatormay be used to synchronize the onset of a ventilation cycle with patienteffort. Such synchrony results in improved patient ventilation. In somecases, a ventilation cycle is triggered to begin once the filteredpatient effort signal is less than zero. In other cases, a ventilationcycle is triggered to begin once the filtered patient effort signalreaches a predefined negative threshold value or positive thresholdvalue. It should be noted that while the filtered patient effort signalis used in the preceding example, that one or more other signals may besimilarly used. For example, prediction error signal, z−{circumflex over(z)} may also be used as it is similarly correlated with actual patienteffort. Based on the disclosure provided herein, one of ordinary skillin the art will recognize a variety of other signals that may be used toinitiate a ventilation cycle.

Alternatively, it is determined whether the updated prediction ofpatient effort indicates an end condition (block 540). Where an endcondition is indicated (block 540), a previously started ventilationcycle is triggered to terminate (block 545). As an example, the updatedprediction of patient effort may be the same filtered patient effortsignal used to trigger the onset of inspiration. As the filtered patienteffort signal is a function of the derivative of patient effort, the endof inspiration is indicated when the filtered patient effort signalbecomes greater than zero (e.g., exhibits a positive zero crossing wherethe signal transitions from a negative value to a positive value). Suchan indicator may be used to synchronize the termination of a ventilationcycle with patient effort, and thereby provide improved patientventilation. In some cases, a ventilation cycle is triggered to end oncethe filtered patient effort signal is greater than zero. In other cases,a ventilation cycle is triggered to end once the filtered patient effortsignal reaches a predefined negative threshold value or positivethreshold value. Again, it should be noted that while the filteredpatient effort signal is used in the preceding example, that one or moreother signals may be similarly used. For example, prediction errorsignal, z−{circumflex over (z)} may also be used as it is similarlycorrelated with actual patient effort. Based on the disclosure providedherein, one of ordinary skill in the art will recognize a variety ofother signals that may be used to terminate a ventilation cycle.

Turning to FIG. 7, a timing diagram 600 shows the process of triggeringmultiple ventilation cycles based on a proxy of patient effort. In thiscase, the proxy of patient effort is the filtered patient effort signal(φ_(d)) 610. An actual patient effort signal (P_(p)) 620 is shown todemonstrate the synchrony achievable using different embodiments of thepresent invention. It should be noted that while filtered patient effortsignal 610 is shown as the ventilation trigger, that one or more othersignals may be similarly used. For example, prediction error signal,z−{circumflex over (z)}, may also be used as it is similarly correlatedwith actual patient effort. Based on the disclosure provided herein, oneof ordinary skill in the art will recognize a variety of other signalsthat may be used to effectuate triggering.

As shown, the transition of filtered patient effort signal 610 through anegative zero crossing point 612 a corresponds to the beginning of anactual patient inspiration effort 622 a. A subsequent positive zerocrossing point 614 a corresponds to the onset of exhalation 624 a. Thisprocess is depicting for a number of ventilation cycles. Consistent withtiming diagram 600, a positive zero crossing of filtered patient effortsignal 610 may be used to trigger the beginning of a ventilation cycle,and a negative zero crossing of filtered patient effort signal 610 maybe used to trigger the end of a ventilation cycle.

FIG. 8 includes a timing diagram 710 showing a process of triggering offof a pressure sensor corresponding to p_(y), a timing diagram 720showing a process of triggering off of an estimated patient effortsignal, p_(y)−{circumflex over (p)}_(y), and a timing diagram 730showing a process of triggering off of another signal correlated topatient effort, z−{circumflex over (z)}. As shown by timing diagram 710,the pressure sensor exhibits a noise level 711 with a trigger threshold713 set a noise buffer amount 712 below the expected noise level 711 toavoid false triggering. As shown, the pressure corresponding to p_(y)eventually drops below trigger threshold 713 resulting in a detectedinspiration onset 714 (represented a vertical dashed line). Detectedinspiration threshold 714 occurs a delay period 715 after an actualinspiration onset 716 (represented by a vertical dashed line). As can beseen from timing diagram 710, the magnitude of delay period 715 is afunction of noise level 711 and noise buffer amount 712.

Noise associated with a pressure measurement is not necessarilycorrelated with that associated with flow measurements. By combininginformation derived from both pressure and flow measurements in thedevelopment of an estimated patient effort signal, the amount of noiseexpected is typically reduced when compared with the noise expected whenonly a single measurement is used. A noise buffer amount is often chosenbased on the magnitude of expected noise. Thus, in some embodiments ofthe present invention, both the expected noise level and noise bufferamount are less than that exhibited in single measurement systems. Thereduction of these variables allows for a detected inspiration that iscorrelated more closely in time with an actual inspiration onset. Timingdiagrams 720, 730 graphically depict such a reduced trigger delay.

Following timing diagram 720, the estimated patient effort signal,p_(y)−{circumflex over (p)}_(y), exhibits a relatively small noise level721 with a trigger threshold 723 set a noise buffer amount 722 above theexpected noise level 721 to avoid false triggering. As shown, theestimated patient effort signal eventually exceeds trigger threshold 723resulting in a detected inspiration onset 724 (represented a verticaldashed line). Detected inspiration onset 724 occurs a delay period 725after an actual inspiration onset 726 (represented by a vertical dashedline). Delay period 725 is less than that which results when only asingle point of measurement is used. Similarly, following timing diagram730, the estimated patient effort signal, z−{circumflex over (z)},exhibits a relatively small noise level 731 with a trigger threshold 733set a noise buffer amount 732 above the expected noise level 731 toavoid false triggering. As shown, the estimated patient effort signaleventually exceeds trigger threshold 733 resulting in a detectedinspiration onset 734 (represented a vertical dashed line). Detectedinspiration onset 734 occurs a delay period 735 after an actualinspiration onset 736 (represented by a vertical dashed line). Delayperiod 735 is less than that which results when only a single point ofmeasurement is used.

Turning to FIG. 9, a flow diagram 800 shows a method for providingventilation in proportion to patient effort in accordance with variousembodiments of the present invention. Following flow diagram 800, apressure is measured (block 805), an inlet flow is measured (block 810),and an outlet flow is measured (block 815). In some cases, the pressureis measured in a tube connecting a ventilator to a person beingventilated. In some cases, the pressure is measured near a gas inletand/or near a gas outlet. In other cases, the pressure is measured neara junction of the gas inlet with the gas outlet. In various cases, thepressure measurement is a single point pressure measurement, while inother cases the pressure measurement is a multiple point pressuremeasurement and the measured pressure is a mathematical combination oftwo or more pressure measurements. Measuring the inlet flow may includemeasuring the flow of a single gas, or measuring the flows of two ormore gases and aggregating the multiple flow values. Measuring theoutlet flow may include, but is not limited to, measuring the flow ofgas at the outlet of the ventilation system. The outlet flow issubtracted from the inlet flow at a particular instance to generate aninstantaneous net flow (block 820).

The net flow and measured pressure for a given instant are used tocalculate an updated prediction of patient effort (block 825). Thisprocess may be done using the approach discussed above in relation toFIG. 4. Desired gas delivery parameter(s) of gas to be delivered by theventilator an instant corresponding to the calculated patient effortis/are then calculated (block 840). In some embodiments of the presentinvention, the gas delivery parameters are flow and/or pressure. In thiscase, a desired pressure and flow of gas delivery are each a function ofpatient effort. For example, where patient effort is determined to be avalue at an instant x described by a function ƒ(x), then the calculatedpressure may be described at an instant using the function g(f(x)) andthe calculated flow at an instant may be described by the functionh(f(x)). In one particular embodiment of the present invention, thefunction g and the function h are each constant multipliers. In such acase, the calculated pressure at an instant x is k₁f(x) and thecalculated flow at the instant x is k₂f(x), where k₁ is the constantcorresponding to pressure and k₂ is the constant corresponding to flow.Based on the disclosure provided herein, one of ordinary skill in theart will recognize other functions g functions h that may be used inrelation to different embodiments of the present invention. The pressureused as a metric for delivering gas may be, but is not limited to, wyepressure or patient lung pressure. The flow used as a metric fordelivering gas may be, but is not limited to, patient lung flow or inletgas flow.

It is then determined whether the updated prediction of patient effortindicates an inspiration phase (block 830). In some embodiments of thepresent invention, an inspiration phase is indicated where thederivative of patient effort {dot over (p)}_(P) is greater than zeroWhere an inspiration phase is indicated (block 830), gas is delivered toa recipient in accordance with the gas delivery parameters previouslycalculated (lock 835). Again, gas delivery parameters may include, butare not limited to, pressures and flows of gas or gas components (e.g.,oxygen, air, nitrogen, helium, etc.) to be delivered to a patient.Otherwise, where an inspiration phase is not indicated (block 830), gasdelivery is not provided. Such an approach provides for gas delivery ata rate and/or pressure as a function of the patient's effort. Such anapproach provides for increased patient comfort as well as lessinterference with a patient's own attempts at breathing.

Turning to FIG. 10, four timing diagrams 910, 920, 930, 940 graphicallydepict providing ventilation in proportion to patient effort inaccordance with one or more embodiments of the present invention. Timingdiagram 910 depicts patient effort as a function of time, and timingdiagram 920 depicts a derivative of patient effort as a function oftime. As shown, when the derivative of patient effort is greater thanzero (corresponding to an inspiration phase), patient effort isdescribed as a function ƒ(x). It should be noted that while timingdiagram 910 shows patient effort as the same function repeating overtime, that a first instance of f₁(x) 912 may differ substantially fromthe second instance of f₂(x) 914 depending upon the breathing pattern ofthe particular patient.

A timing diagram 930 depicts an effort by a ventilator to increase thepressure at the wye connection to offset a pressure decrease caused bypatient effort. As shown, during the inspiration phase (i.e., when thederivative of patient effort is greater than zero), the ventilatorattempts to raise the pressure at the wye connection as a function ofpatient effort, g(f₁(x)) 932. On a subsequent breath, the ventilatorattempts to raise the pressure at the wye as a function of patienteffort, g(f₂ (x)) 934. In this particular case, the function g is aconstant k₁, however, other time varying functions may be used inaccordance with different embodiments of the present invention.

Similarly, during the inspiration phase, the ventilator increases theflow of gas to a patient as a function of patient effort, h(f₁(x)) 942.On a subsequent breath, the ventilator increases the flow of gas to apatient as a function of patient effort, h(f₂(x)) 944. In thisparticular case, the function h is a constant k₂, however, other timevarying functions may be used in accordance with different embodimentsof the present invention. In some cases, the functions g and h may beproportional or inversely proportional to patient effort. It should benoted that in the sense that gas delivery is provided as a function ofpatient effort, that patient effort may be determined based directly onpatient effort (i.e., patient interpleural pressure), or on a first orhigher order derivative of patient effort.

Turning to FIG. 11, an exemplary graphical interface 1000 showing thedisplay of patient effort corresponding to an actively breathing patientin accordance with some embodiments of the present invention. Graphicalinterface 1000 includes a graphical display of filtered patient effort(φ_(d)) 1010, and patient effort (p_(p)) 1020 each as a function oftime. It should be noted that other indications of patient effort may bedisplayed in addition to those depicted or in place of those depicteddepending upon the particular embodiment of the present invention.

In the depicted embodiment, time is displayed across a horizontal axisand the value of the respective patient effort value is displayed acrossa left axis. As time proceeds, the time increments across the horizontalaxis are updated to reflect a window around the current time. Inaddition, two user movable vertical bars 1012, 1022 are disposed overgraph 1010 and graph 1020. This allows a user to place a begin bar 1012and an end bar 1022 at particular times to measure an event. The timedifference between begin bar 1012 and end bar 1022 may be displayed tothe user, along with the value of filtered patient effort and patienteffort at the respective instants in time. In some cases, begin bar 1012and end bar 1022 may be used via a keyboard command or a mouse command.Based on the disclosure provided herein one of ordinary skill in the artwill recognize a variety of I/O that may be used to manipulate begin bar1012 and end bar 1022 in relation to graphs 1010, 1020.

In addition, various metrics relating to the graphically displayedpatient effort may be calculated and displayed via graphical interface1000. For example, a mean time between breaths 1030 may be calculatedand displayed. Such a mean time may be calculated based on a definednumber of breaths, where a time between each of the breaths iscalculated from the end of expiration to the beginning of subsequentinspiration. Based on the disclosure provided herein, one of ordinaryskill in the art will appreciate a variety of approaches that may beused to calculate mean time between breaths in accordance with differentembodiments of the present invention. As another example, a peakbreathing effort 1040 may be displayed. Peak breathing effort 1040 maybe the maximum value recorded on either of graph 1010 or graph 1020 overthe course of a defined number of breaths depending upon the particularimplementation. As yet another example, peak effort per breath 1050 maybe displayed. Peak effort per breath 1050 may indicate the peak value ofeither graph 1010 or graph 1020 for a most current breath. Alternativelyit may indicate the peak value of either graph 101 or graph 1020 for abreath identified by begin bar 1012. As yet a further example, aduration of last inspiration 1060 may be displayed. Duration of the lastinspiration 106 indicates a time from when the onset of inspiration wasdetected until the end of inspiration was detected for the most recentbreath. In one case, this may be achieved by detecting when a firstderivative of the patient effort exceeds a threshold until it returnsbelow the threshold. As another example, a duration of the lastexpiration 1070 may be displayed. In some cases, duration of the lastexpiration 1070 may be calculated by detecting when a first derivativeof the patient effort falls below a threshold until the time when thefirst derivative returns above the threshold. As another example, anaverage duration of inspiration 1080 and an average duration ofexpiration 1090 may be displayed. The may be calculated by averaging anumber of the previously discussed expiration durations and inspirationdurations.

Turning to FIG. 12, an exemplary graphical interface 1100 showing thedisplay of a respiratory parameter corresponding to an activelybreathing patient in accordance with some embodiments of the presentinvention. In particular, a graph 1110 depicts an estimated value of thepatient resistance parameter as a function of time. In some embodiments,the patient resistance parameter is referred to as “estimated Rp”because it is the result of calculation as distinguished from the actualvalue of the patient resistance. It should be noted that while graphicalinterface 1100 is described as showing estimated Rp, that otherrespiratory parameters may be displayed in accordance with differentembodiments of the present invention. For example, graphical interface1100 may be augmented to display lung compliance or leakage parameters,with these additionally displayed parameters determined using the sameor similar set of equations as described herein. Based on the disclosureprovided herein, one of ordinary skill in the art will recognize avariety of respiratory parameters that may be displayed. In some cases,the displayed respiratory parameters may be used by a monitoringclinician for real time assessment of a patient. Alternatively, or inaddition, the displayed respiratory parameters may be used to determinea potential system malfunction or to indicate a disconnect of thepatient from the ventilator. As one particular example, a dramaticincrease in Rp may indicate a partial obstruction. Based on thedisclosure provided herein, one of ordinary skill in the art willrecognize a variety of advantages that may be achieved in accordancewith one or more embodiments of the present invention.

As shown, time is displayed across a horizontal axis and the value ofestimated Rp is displayed across a left axis. In some embodiments, astime proceeds, the time increments across the horizontal axis areupdated to reflect a window around the current time. Additionally, insome embodiments, two user movable vertical bars 1112, 1113 are disposedover graph 1110. This allows a user to place a begin bar 1112 and an endbar 1113 at particular times to measure an event. The time differencebetween begin bar 1112 and end bar 1113 may be displayed to the user,along with the value of filtered patient effort and patient effort atthe respective instants in time. In some cases, begin bar 1112 and endbar 1113 may be used via a keyboard command or a mouse command. Based onthe disclosure provided herein one of ordinary skill in the art willrecognize a variety of I/O that may be used to manipulate begin bar 1112and end bar 1113 in relation to graph 1110.

In this particular example, for an initial period 1120 estimated Rp isinitialized with a value of five (5) cmH₂O/lps. At this time, the actualvalue of Rp is nearer to thirty (30) cmH₂O/lps. Over a period of time,the algorithm used to determine the value of estimated Rp adaptivelyadjusts until the estimated value approximates the actual value for Rpduring a period 1130. Sometime around the fifty (50) second mark, anobstruction is removed from the ventilation system resulting in adramatic decrease in the actual value of Rp. At this point, thealgorithm adaptively adjusts by lowering the value of estimated Rp untilthe estimated value approximates the actual value. During a period 1140,the value of estimated Rp remains approximately constant near the actualvalue of Rp.

In addition, various metrics relating to the graphically displayedresistance parameter may be calculated and displayed via graphicalinterface 1100. For example, a current Rp value 1150 may be displayed,and an average Rp value 1160 may be displayed. Average Rp value 1160 maybe calculated by averaging a number of values for Rp over a particulartime period. In addition, a visual alarm 1170 may be displayed. Such avisual alarm may be triggered whenever a predefined increase or decreasein the value of estimated Rp is detected. It should be noted thatgraphical interface 1100 may be augmented to display a variety of otherinformation.

The present invention provides novel systems, methods and devicesdelivering a gas in proportion to a patient effort. While detaileddescriptions of one or more embodiments of the invention have been givenabove, various alternatives, modifications, and equivalents will beapparent to those skilled in the art without varying from the spirit ofthe invention. Therefore, the above description should not be taken aslimiting the scope of the invention, which is defined by the claims.

What is claimed is:
 1. A ventilation system, the ventilation systemcomprising: a graphical display; a processor communicably coupled to acomputer readable medium, wherein the computer readable medium includesinstructions executable by the processor to: receive a measured pressurevalue; receive a net flow value; calculate a patient effort value basedon a relationship between the measured pressure value, the net flowvalue, and an estimated normalized prediction error, wherein theestimated normalized prediction error is based at least in part on acurrent estimated value of a parameter vector; and plot the patienteffort value to the graphical display.
 2. The system of claim 1, whereinthe patient effort value is an estimate of actual patient effort.
 3. Thesystem of claim 1, wherein the patient effort value is a firstderivative of the actual patient effort.
 4. The system of claim 1,wherein the patient effort value is a filtered patient effort.
 5. Thesystem of claim 1, wherein the instructions are further executable bythe processor to: calculate a mean time between breaths based on thepatient effort value; and display the mean time between breaths to thegraphical display.
 6. The system of claim 1, wherein the instructionsare further executable by the processor to: identify a peak breathingeffort based on the patient effort value; and display the peak breathingeffort to the graphical display.
 7. The system of claim 1, wherein theinstructions are further executable by the processor to: identify a peakeffort for a particular breath based on one or more patient effortvalues calculated during the particular breath; and display the peakeffort for the particular breath to the graphical display.
 8. The systemof claim 1, wherein the instructions are further executable by theprocessor to: calculate a duration of last inspiration based on thepatient effort value; and display the duration of last inspiration tothe graphical display.
 9. The system of claim 1, wherein theinstructions are further executable by the processor to: calculate aduration of last expiration based on the patient effort value; anddisplay the duration of last expiration to the graphical display. 10.The ventilation system of claim 1, wherein the patient effort value isfurther based on a combination of one or more intermediate valuescalculated using the measured pressure value and the net flow value, theone or more intermediate values selected from: a filtered pressure valueand a regression vector.
 11. The ventilation system of claim 1, whereinthe relationship is a parameterized system input to output relationship.12. The method of claim 11, wherein the parameterized system input tooutput relationship is the regression form: z=Θφ+φ_(d), wherein z is afiltered pressure value, Θ is a current estimated value of a parametervector, φ is at least apart of regression vector, and φ_(d) is afiltered patient effort.
 13. The method of claim 11, wherein theparameterized system input to output relationship is derived from atransfer function.
 14. The ventilation system of claim 13, wherein thetransfer function is derived from the model: $\begin{bmatrix}{\overset{.}{p}}_{Y} \\{\overset{.}{p}}_{L}\end{bmatrix} = {{\begin{bmatrix}{- \frac{1}{C_{T}R_{P}}} & \frac{1}{C_{T}R_{P}} \\\frac{1}{C_{L}R_{P}} & {- \frac{1}{C_{L}R_{P}}}\end{bmatrix}\left\lbrack \begin{matrix}p_{Y} \\p_{L}\end{matrix} \right\rbrack} + {\quad{{\begin{bmatrix}\frac{1}{C_{T}} & \frac{1}{C_{T}} & {- \frac{1}{C_{T}}} \\0 & 0 & 0\end{bmatrix}\begin{bmatrix}q_{AIR} \\q_{O\; 2} \\q_{E}\end{bmatrix}} + {\begin{bmatrix}0 & {- \frac{1}{C_{T}}} & 0 \\1 & 0 & {- \frac{1}{C_{T}}}\end{bmatrix}\begin{bmatrix}{\overset{.}{p}}_{P} \\q_{Tleak} \\q_{Pleak}\end{bmatrix}}}}}$ wherein p_(y) is a value for a wye gas pressure,p_(L) is a value of a pressure in a patient's lungs, {dot over (p)}_(y)is a value for a first derivative of a wye gas pressure, {dot over(p)}_(L) is a value for a first derivative of pressure in the patient'slungs, C_(T) is a value for a tubing compliance, C_(L), is a value for alung compliance, R_(P) is a value for a patient resistance, q_(air) is avalue for an inlet flow of air, q₀₂ is a value for an inlet flow ofoxygen, q_(E) is a value for an outlet gas flow, q_(Tleak) is a valuefor gas flow associated with tubing leakage, q_(Pleak) is a value forgas flow associated with leakage in the patient, and {dot over (p)}_(P)is a value for the derivative of patient effort.
 15. A method forproviding graphical respiratory feedback, the method comprising:providing a graphical display; measuring a pressure and providing ameasured pressure; measuring an inlet flow and an outlet flow, andproviding a measured net flow; using a relationship between a firstvalue related to the measured pressure, a second value related to themeasured net flow and an estimated normalized prediction error, whereinthe estimated normalized prediction error is based at least in part on acurrent estimated value of a parameter vector, to calculate an estimateof patient effort from the measured pressure and measured net flow; andrepeatedly displaying the estimate of patient effort as a function oftime via the graphical display.
 16. The method of claim 15, wherein theestimate of patient effort is an estimate of actual patient effort foran associated time instant.
 17. The method of claim 15, wherein theestimate of patient effort is an estimate of a first derivative of theactual patient effort for an associated time instant.
 18. The method ofclaim 15, wherein the estimate of patient effort is a filtered actualpatient effort.
 19. The method of claim 15, wherein the method furthercomprises: calculating various ventilation characteristics based on theestimate of patient effort, wherein the various ventilationcharacteristics are selected from: a mean time between breaths, a peakbreathing effort, a peak effort for a particular breath, a duration oflast inspiration, a duration of last expiration, an average duration ofinspiration, and an average duration of expiration.
 20. The method ofclaim 15, wherein the method further comprises: graphically displayingvarious ventilation characteristics based on the estimate of patienteffort, wherein the various ventilation characteristics are selectedfrom: a mean time between breaths, a peak breathing effort, a peakeffort for a particular breath, a duration of last inspiration, aduration of last expiration, an average duration of inspiration, and anaverage duration of expiration.
 21. The method of claim 15, wherein therelationship is defined by a parameterized system input to outputrelationship in the regression form z=Θ^(T)φ+φ_(d), and wherein theinput to output relationship is derived from a transfer function,wherein z is a filtered pressure value, Θ is a current estimated valueof a parameter vector, φ is at least a part of regression vector, andφ_(d) is a filtered patient effort.
 22. The method of claim 21 whereinthe transfer function is derived from a model: $\begin{bmatrix}{\overset{.}{p}}_{Y} \\{\overset{.}{p}}_{L}\end{bmatrix} = {{\begin{bmatrix}{- \frac{1}{C_{T}R_{P}}} & \frac{1}{C_{T}R_{P}} \\\frac{1}{C_{L}R_{P}} & {- \frac{1}{C_{L}R_{P}}}\end{bmatrix}\left\lbrack \begin{matrix}p_{Y} \\p_{L}\end{matrix} \right\rbrack} + {\quad{{\begin{bmatrix}\frac{1}{C_{T}} & \frac{1}{C_{T}} & {- \frac{1}{C_{T}}} \\0 & 0 & 0\end{bmatrix}\begin{bmatrix}q_{AIR} \\q_{O\; 2} \\q_{E}\end{bmatrix}} + {\begin{bmatrix}0 & {- \frac{1}{C_{T}}} & 0 \\1 & 0 & {- \frac{1}{C_{T}}}\end{bmatrix}\begin{bmatrix}{\overset{.}{p}}_{P} \\q_{Tleak} \\q_{Pleak}\end{bmatrix}}}}}$ wherein p_(y) is a value for a wye gas pressure,p_(L) is a value of a pressure in a patient's lungs, {dot over (p)}_(y)is a value for a first derivative of a wye gas pressure, {dot over(p)}_(L) is a value for a first derivative of pressure in the patient'slungs, C_(T) is a value for a tubing compliance, C_(L) is a value for alung compliance, R_(P) is a value for a patient resistance, q_(air) is avalue for an inlet flow of air, q₀₂ is a value for an inlet flow ofoxygen, q_(E) is a value for an outlet gas flow, q_(Tleak) is a valuefor gas flow associated with tubing leakage, q_(Pleak) is a value forgas flow associated with leakage in the patient, and {dot over (p)}_(P)is a value for the derivative of patient effort.
 23. A ventilationsystem, the ventilation system comprising: a gas inlet; a gas outlet; atube coupling the gas inlet and the gas outlet; a pressure sensor,wherein the pressure sensor is operable to provide a measured pressurevalue indicating a pressure in the tube; a first flow sensor, whereinthe first flow sensor is operable to provide an inlet flow valueindicating a flow associated with the gas inlet; a second flow sensor,wherein the second flow sensor is operable to provide an outlet flowvalue indicating a flow associated with the gas outlet; a graphicaldisplay; and a processor communicably coupled to a computer readablemedium, wherein the computer readable medium includes instructionsexecutable by the processor to: receive a measured pressure value;receive a net flow value; calculate a patient effort value based on arelationship between patient effort, an estimated normalized predictionerror, wherein the estimated normalized prediction error is based atleast in part on a current estimated value of a parameter vector, themeasured pressure value, and the net flow value; calculate a gasdelivery metric that varies as a first function of the patient effortvalue; determine an inhalation phase based on the patient effort value;and plot the patient effort value to the graphical display.